Engorgement vs clogs- who wins?

So this is what I’m struggling with …

I hate the feeling of being engorged (I’m 4 weeks pp!) but I’ve read that if baby isn’t ready to eat to avoid pumping as that will just rev up supply. Makes sense.

But! I’ve also read that not emptying can cause clogs?? So who wins? Do I ride out the engorgement with gentle massage, ice, ibuprofen, or pump to relieve?

This has been plaguing me, esp since my baby rarely wants both breasts at one feeding. It means hours can go by on the alternate breast (I.e if he eats on the left breast at 9am, then right breast at 11:30am, it can not be until 1pm he’s back on the left breast.) would anything change here with this? Thanks!